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A block of mass M and height h is moving on a rough surface of coifficent of friction 0.5 .The block is moving with a velocity v at some instant. if we balance the torque due to frictional force and normal force about the center of mass of the block we obtain x=h/4.hence the normal force acts at h/4 from the center of mass. however if we consider the point C there is a net torque about it due to normal force and gravity. hence the body should rotate about C. but it does not. why is that?

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Because there is a net force on the block, it must be accelerating. This means point $C$ is at rest in a non-inertial frame, and we will see fictitious forces appear in this frame.

The fictitious force will be in the opposite direction of the acceleration, proportional to the mass. When you apply this force at the center of mass, you will find the torques once again cancel out.

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    $\begingroup$ I was a bit confused until I realized the block has some initial velocity and is slowing down due to the frictional force. $\endgroup$ – Carl Witthoft Dec 17 '15 at 14:47

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